What was already known
Geodesic-ball volume comparison does not imply boundary-area comparison for arbitrary domains. The target is the full isoperimetric inequality, beyond known dimensions and special classes.
What changed and why it matters
Extends the stated isoperimetric comparison to all dimensions and arbitrary finite-perimeter sets under its hypotheses.
The AI contribution
OpenAI attributes these manuscripts to its internal model. The entry does not infer individual human contributions beyond that publisher attribution.
Limitations
The curvature, completeness, and simple-connectivity hypotheses are retained. Euclidean equality rigidity is stated for bounded positive-volume sets; no unrestricted equality classification is inferred. Preprint. This is a source-statement and significance assessment, not a proof audit. No independent checking or successful formal compilation is asserted by this entry.
Verification evidence
Evidence labels show what supports the claim. Importance rates its impact if correct.
Author claim
The publisher reports the scoped result. AIProofWatch has not independently validated its correctness.
Accessible artifact / proof
The original written argument is accessible. Availability does not establish a successful proof check or Lean verification.
Correction and publication history
Historical report added after statement, scope, and importance review. No proof audit or formal checking asserted; subscriber alerts disabled.
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